Narrow Results

Voronoi tessellations and their dual Delaunay tetrahedral tessellations provide versatile representations of three-dimensional structures of proteins, allowing a strict definition of neighborhoods of the different amino acids, considered as rigid entities. They give geometrical and topological information coded in the adjacency matrix (often called contact map in biology). Using this approach, this paper presents a two-dimensional description of internal surfaces, which are tools used to understand the conformation of globular proteins. These surfaces are triangulated surfaces tiled by faces of Delaunay tetrahedra. Two simple types of surfaces are presented, characterized by their topology: disk-like or torus-like. The torus-like surface is relevant in the description of secondary structures. The disk-like surface characterizes the collapse of the chain onto itself.